Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI-09)
Transfer Learning Using Task-Level Features
with Application to Information Retrieval
Rong Yan
IBM T. J. Watson Research
Hawthorne, NY, USA
Jian Zhang
Purdue University
West Lafayette, IN, USA
yanr@us.ibm.com
jianzhan@stat.purdue.edu
Abstract
We propose a probabilistic transfer learning model
that uses task-level features to control the task mixture selection in a hierarchical Bayesian model.
These task-level features, although rarely used in
existing approaches, can provide additional information to model complex task distributions and
allow effective transfer to new tasks especially
when only limited number of data are available.
To estimate the model parameters, we develop an
empirical Bayes method based on variational approximation techniques. Our experiments on information retrieval show that the proposed model
achieves significantly better performance compared
with other transfer learning methods.
1 Introduction
Recent years have seen a growing interest in developing algorithms to learn multiple related tasks and dynamically transfer
existing models to new tasks. This is known as transfer learning [Thrun and Pratt, 1998], or multi-task learning [Caruana,
1997]. It has been empirically as well as theoretically shown
that transfer learning can significantly improve the learning
performance especially when only a small number of data are
available for new tasks. Transfer learning has many practical
applications, and one such example is information retrieval.
In more details, information retrieval can be cast into binary classification that considers the relevant query-document
pairs as positive data and irrelevant pairs as negative data. By
viewing each query as a separate task, we can reformulate the
retrieval task into a transfer learning problem, which aims to
predict the relevance of each document for a new query based
on the manual relevance judgment from the training queries.
Many transfer learning methods assume that the model parameters are generated from a uni-modal distribution (such as
normal) for all given tasks. However, such an assumption is
very likely to be violated in practice. As a matter of fact, tasks
in many domains tend to be grouped into a number of clusters,
and different tasks can be associated with different clusters.
In such cases, it is of great importance for the transfer learning algorithms to effectively capture task-cluster associations
and route a new task to the correct cluster. Although a simple
mixture model instead of a uni-modal distribution can capture the above multi-cluster situation, the goal is still difficult
to achieve when each task only possesses a limited number of
training examples. Even worse, a new task can appear without any training examples at all. Unfortunately, transferring
to a new task with few examples is typical in real applications
such as information retrieval.
To approach this issue, we consider incorporating into
transfer learning a set of features which can directly represent
the properties of the task itself, called “task-level features”,
in additional to the commonly-used data features generated
from training examples. Task-level features can be extracted
in a flexible way. In information retrieval, task features can
be defined as the properties of user queries, such as whether
the query contains person names or not. Similarly, task features can also be generated from user profiles in collaborative filtering task, and school-level information for predicting
student exam scores [Bakker and Heskes, 2003]. Intuitively,
these task features provide helpful evidence to pinpoint which
cluster a given task belongs to, especially when only a limited
number of data examples are available for individual tasks.
But the values of task features have not been fully explored
in the previous work of transfer learning.
In this paper, we propose a probabilistic transfer learning(TL) model by introducing task-level features to a hierarchical Bayesian model for classification. We call it the
TL-TF model in the rest of the paper. This model assumes
the model parameters for different tasks are generated from a
linear combination of basic logistic regression classifiers together with a small set of hidden sources. The distribution of
hidden sources of each task is controlled by its task features,
while the combination weights and the model parameters in
basic classifiers are learned from the data examples. To estimate the parameters of TL-TF, we also develop an empirical Bayes method based on variational approximation techniques. When transferring to a new task, the weights of task
mixtures can be directly derived from its task features, and
thus the classification outputs can be computed without using
any additional training data from the new task. As the first attempt to apply transfer learning with task features to information retrieval, our experiments show that the proposed model
is much more effective than other TL methods that either discard the task features, or treat task features as another set of
data features.
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2 Related Work
In the literature, transfer learning has also been known as
“multi-task learning” and “learning to learn”. Many methods
have been proposed for transfer learning and multi-task learning, such as neural networks [Caruana, 1997],transformation
methods [Breiman and Friedman, 1997], regularization learning methods [Evgeniou et al., 2005; Ando and Zhang, 2004],
hierarchical Bayesian models [Heskes, 2000; Yu et al., 2005;
Zhang et al., 2005] and etc.
In particular, the proposed model is closely related to the
work based on hierarchical Bayesian models, which provide
a flexible yet compact representation of the structure in the
data space. Thus, they allow models to fit existing data well
and generalize well on unseen data. For example, [Heskes,
2000] presented a model for multi-task learning by assuming
that response variables of each task follow a normal distribution. Empirical Bayes techniques are used to learn the model
hyper-parameters. In [Yu et al., 2005], Gaussian processes
are applied to model multiple related tasks and a single Gaussian component is used to capture the mean and covariance
of all related tasks. [Zhang et al., 2005] further proposed a
latent variable model for multi-task learning which assumes
that tasks are sparse linear combination of basic classifiers. A
more recent work [Xue et al., 2007] proposed a Dirichlet process based hierarchical Bayesian model for learning multiple
related classifiers. However, none of above models take the
task-level features into account in the learning process.
By utilizing task features in a softmax gating function,
[Bakker and Heskes, 2003] augmented the Bayesian neural
network model to handle multi-task learning with real-valued
outputs and additive noise. This approach has shown to be effective in multiple data collections. However, this study was
mainly focusing on regression in a non-transfer setting. More
recently, [Bonilla et al., 2007] presented a kernel multi-task
regression method using Gaussian process with task features.
In contrast, the proposed approach is a hierarchical Bayesian
model with focus on classification problems under the transfer learning setting, which is more typical for applications
such as information retrieval. Moreover, to our best knowledge, our work is the first attempt to apply transfer learning
with task-level features to the information retrieval domain.
3 Transfer Learning with Task-Level Features
In this section, we describe the details of the proposed TL-TF
model by introducing mixture modeling and task-level features to hierarchical Bayesian models. First, let us assume
there are K classification tasks. Each task is associated with
a training data set D(k) = {X(k) , y(k) }, where the training
(k)
(k)
data are X(k) = [x1 , . . . , xnk ]T ∈ Rnk ×F and the labels
(k)
(k)
are y(k) = [y1 , . . . , ynk ]T . y(k) ∈ {0, 1}nk ×1 for the classification tasks and y(k) ∈ Rnk ×1 for the regression tasks.
Furthermore, for each task we are able to obtain a set of tasklevel features t(k) ∈ RP ×1 that describe the task properties.
These features can be automatically extracted from the task
description without knowing the data examples, such as the
number of persons mentioned in queries in information retrieval and the age of users in collaborative filtering.
One building block for transfer learning is to define the
learning models for each individual task. In this paper, we
consider using the parametric model f (k) (x) = f (k) (x|θ (k) )
to generate the data labels for each task, where the parameter
θ(k) is used to index the prediction function f (k) .1 Given
the parameter θ (k) , we can derive the following likelihood
models for classification,
(k)
yi
(k)
∼ Bernoulli(g(θ(k) , xi ))
(1)
−1
where g(t) = (1 + exp(−t)) is the logistic function and
x, y is used to denote the inner product between x and y.
This model becomes logistic regression if the model parameters θ(k) are estimated independently on each single task.
In order to learn multiple related tasks more effectively,
we can transform individual task learning process into a joint
learning problem, which explains the relatedness of multiple tasks through some hidden sources s(k) . To handle the
multi-cluster task distribution, we assume the hidden source
variable s(k) is sampled from a multinomial distribution and
use it to indicate which mixture component the task belongs
to. Given that a set of task-level features t(k) are available for
each task, we further assume the distribution parameters of sk
are determined by its task features. Then a generative model
can be constructed for θ(k) ’s in such a way that not only task
dependency structure can be captured and jointly modeled,
but also the information contained in t(k) can be effectively
utilized. Formally, we can have the following hierarchical
Bayesian model for generating θ(k) ’s:
θ (k)
s(k)
=
∼
Λs(k) + e(k)
Multinomial (p1 , . . . , pH )
e(k)
∼
Normal (0, Ψ)
ph
=
exp(γ Th t(k) )
T (k) )
h exp(γ h t
(2)
where θ (k) ∈ RF ×1 are the model parameters for the k th
task, t(k) ∈ RP ×1 are the task features, s(k) ∈ RH×1 are the
hidden source vector2 where H is the number of task clusters
and γ h denotes the distribution parameters for the softmax
function ph , Λ ∈ RF ×H is the linear transformation matrix
and e(k) is a multi-variate Gaussian noise vector with a covariance matrix Ψ ∈ RF ×F . To further simplify derivation,
we use Γ = [γ 1 , . . . , γ H ] ∈ RP ×H to denote the parameter
matrix of the multi-class logistic regression where γ h is its hth column, and similar notation is used for Λ = [λ1 , . . . , λH ]
where λh is the h-th column of Λ. Also note that due to
the properties of multi-class logistic regression [Hastie et al.,
2001] we can fix γ 1 to be the all zero vector 0.
The probabilistic model is complete by combining Eqn (1)
and (2). From the model definition, we can find that: 1. θ(k)
Note that it is not necessary to require all f (k) ’s belonging to the
same parametric family, however, parameters θ (1) , . . . , θ (K) ∈ Θ
are assumed to belong to the same metric space.
2
The vector s(k) takes the forms of [0, . . . , 0, 1, 0, . . . , 0] where
only one element is 1 and the rest are 0’s. We also use z (k) ∈
{1, . . . , H} instead of s(k) to denote the 1’s index for simplicity.
1316
1
is assumed to be normally distributed with the same covariance Ψ. Its mean is a linear combination of columns of Λ
shared by all K tasks; 2. The combination weights for Λ are
determined by the latent variable s(k) sampled from a multinomial distribution; 3. s(k) is controlled by the task-level
features t(k) through a multi-class logistic regression model,
where in some sense t(k) serves as a gating function to adapt
the distribution of hidden sources task by task.
Our model has connections to several previous approaches.
For instance, in the case when H = 1 and without considering the task-level features, the proposed model is closely
related to the multi-task linear models proposed in [Yu et
al., 2005]. Furthermore, when H > 1 it is closely related
to the latent independent component analysis (LICA) model
proposed in [Zhang et al., 2005] which assumes the latent
variable s(k) to follow a sparse prior distribution. However,
in contrast to existing approaches, the proposed model distinguishes itself from the fact that task-level features t(k) are
naturally incorporated into the generation process of latent
variables s(k) . This allows us to model the task-mixture association more accurately and predict the mixture assignment
for a new task even when few data examples are provided.
As a next step, we need to transfer the parameters of the
learned model to a new task (e.g., a new query or a new user)
with a limited number of training data or even no training
data. We are interested in investigating whether the learning
of a new task can benefit from generalizing the previous task
parameters and whether the task features can be helpful to
provide more accurate predictions. In this case, it is key to
develop a generative model, e.g. we have to make explicit
assumptions about how tasks are related. We can observe
from our generative model that given the learned parameters
Γ, Λ and Ψ from previous K tasks, we can naturally extend
the generation process for the (K + 1)-th task to be
θ(K+1)
∼
Normal(Λs(K+1) , Ψ)
s(K+1)
∼
Multinomial(p1 , . . . , pH ),
ph
=
exp(γ Th t(k+1) )
,
T (k+1) )
h exp(γ h t
where t(k+1) is the task feature for the new task. Finally, for
a given input data vector x, its prediction is given by
p(y|x) =
H
ph
p(θ (K+1) |λh , Ψ)p(y|x, θ(K+1) )dθ (K+1) .
h=1
If we want to reduce the computational complexity in the prediction step, an alternative is to use the MAP estimation of
θ(K+1) to avoid the computation of the integral, where the
prediction function can be rewritten as,
p(y|x) =
H
4 Learning and Inference
We present the learning and inference algorithms for TL-TF
in this section. Given the model definition of TL-TF, we need
to estimate the parameters Λ, Γ and Ψ. Here we take the
empirical Bayes approach by integrating out the random variables s(k) ’s and θ (k) ’s. Thus, the log-likelihood of the parameters Ω = {Λ, Γ, Ψ} for observed data {X(k) , y(k) , t(k) }K
k=1
is
“
”
log p y(1) , . . . , y(K) | Ω, X(1) , t(1) , . . . , X(K) , t(K)
=
K
X
log
k=1
Z
×
X
p(s(k) |Γ, t(k) )
s
p(θ (k) |Λ, s(k) , Ψ)
nk
Y
(k)
(k)
p(yi |θ (k) , xi )dθ (k) ,
i=1
where p(s(k) |Γ, t(k) ) is the multinomial distribution of the
hidden sources, p(θ(k) |Λ, s(k) ) is a normal distribution with
(k)
(k)
mean λz(k) and covariance matrix Ψ, and p(yi |θ(k) , xi )
is the likelihood function of classification in Eqn (1).
Such an estimation problem can be solved by the EM algorithm, of which the detailed derivations are given as follows.
To be more specific, the goal of learning is to estimate the
parameters Ω by maximizing the log-likelihood over all K
tasks. Since the log-likelihood function involves two set of
hidden variables, i.e., s(k) ’s and θ(k) ’s, EM is applied to iteratively solve a series of simpler problems.
E-step: Given the parameters Ω all tasks are decoupled,
the E-step can be conducted for each task separately. Thus
we only need to consider one task per time and we can omit
the superscript (k) for simplicity. But because it is generally
intractable to do an exact inference for classification problems, we decided to apply variational methods as one type
of approximate inference techniques to optimize the objective function. The basic idea of variational methods is to use
a tractable family of distributions q(θ, s) to approximate the
true posterior distribution. Specifically we assume an auxiliary distribution q(θ, s) = q1 (s)q2 (θ), e.g. the mean field
approximation, as a surrogate to approximate the true posterior distribution p(θ, s|Ω, X, t, y).
Furthermore, we assume that q1 (s) = q1 (s|Φ) has the
form of multinomial distribution with parameters φ =
H
[φ1 , . . . , φH ]T such that φh ≥ 0 and
h=1 φh = 1.
q2 (θ) = q2 (θ|m, V) has the form of a multivariate normal
with mean m and covariance matrix V. We need to find
the best set of variational parameters φ, m and V such that
the following lower bound is maximized, which is equivalent to minimize the KL divergence between q1 (s)q2 (θ) and
p(θ, s|Ω, X, t, y):
≥
ph p(y|x, λh ).
log p(y|Ω, X, t)
X
q1 (s|φ)Eq2 [log p(y, θ, s|Ω, X, t)] + H(s) + H(θ)
s
h=1
=
This formula can be efficiently computed and thus we adopt
it in our following experiments.
1317
H
X
φh {E[log p(z = h|Ω, t) + E[log p(θ|λh , Ψ)]}
h=1
+E[log p(y|θ, X)] + H(s) + H(θ)
where H(θ)
= − q2 (θ) log q2 (θ)dθ is the entropy of θ,
H(s) = − φh log φh is the entropy of s, and the expected
values of the first two terms on the right hand side are
E [p(θ|λ.h , Ψ)]
=
E [log p(s = h|Ω, t)]
=
(a)
(b)
(c)
(d)
n „
X
yi m T x i − ξ i
log g(ξi ) +
2
i=1
“
””
+h(ξi ) xTi (V + mmT )xi − ξi2
≥
where h(t) = (1/2 − g(t))/(2t), g(t) is the logistic function and n is the number of data for the task. By substituting
the additional lower bound back to Eqn(3), we are able to
optimize the lower bound of the log-likelihood function with
respect to V, m, φ to obtain the following E-step:
ξi
V
=
=
[xTi (V + mmT )xi ]1/2
Ψ−1 − 2
n
X
!−1
g(ξi )xi xTi
(3)
(4)
i=1
m
=
φh
∝
!
H
n
X
1X
−1
yi x i + Ψ
φh λ h
V
2 i=1
h=1
„
«
1
T
T
−1
exp γ h t − (m − λh ) Ψ (m − λh )
2
(5)
(6)
These fixed point equations should be repeated over ξi ’s, m,
V and φh ’s until the lower bound is maximized. Upon convergence, we can use the resulting q1 (s|φ)q2 (θ|m, V) as a
surrogate to the true posterior probability p(s, θ|Ω, X, t, y).
M-step: Given the sufficient statistics obtained in the Estep, the M-step can be derived similarly by optimizing the
lower bound of log-likelihood with respect to the model parameters, i.e., Γ,8Λ, Ψ:
“
” 39
2
K X
H
<X
=
exp γ Th t(k)
(k)
´5
` T
φh log 4 P
Γ̂ = arg min
(k)
;
Γ :k=1 h=1
h exp γ h t
#
"P
P
(k)
(k)
K
K
(k)
(k)
k=1 φ1 m
k=1 φH m
(7)
Λ̂ =
,..., P
PK
(k)
(k)
K
k=1 φ1
k=1 φH
!
K
H
X
1 X
(k)
V(k) +
Ψ̂ =
φh (m(k) − λh )(m(k) − λh )T
K
k=1
1. Initialize parameters Λ, Γ and Ψ.
2. E-step: For the k-th task (k = 1, . . . , K):
˜
1 ˆ
1
− log |2πΨ| − Tr Ψ−1 V
2
2
1
− (m − λh )T Ψ−1 (m − λh )
2
exp(γ Th t)
.
log P
T
h exp(γ h t)
However, the derivation is not complete yet because we
cannot derive a closed-form representation
for the term
E[log p(y|θ, X)], where p(y|θ, X) =
i p(yi |θ, xi ) is a
product of logistic likelihood functions. So we resort to another variational technique proposed in [Jaakkola and Jordan,
1997] to compute its lower bound as a function of m and V
by introducing a new variational parameters ξi for the ith example for the given task:
E[log p(y|θ, X)]
Algorithm 1 Empirical Bayes method for classification tasks
3. M-step: Update parameters according to Eqn(7)
4. Continue steps 2-3 until convergence.
5 Experiments: Information Retrieval
In this section, we examine the effectiveness of the proposed model for an information retrieval task on large-scale
video collections. We compared the proposed TL-TF model
with several baseline models, including a single task learning
(STL) model by directly estimating the likelihood in Eqn (1),
a transfer learning model with a single cluster (TL-SC) and
a TL model with multiple clusters that does not utilize any
task features(TL-MC). To compare in a fair manner, we also
evaluate another multi-cluster TL model that combines task
features with the set of data features without using a taskdependent gating function in Eqn(2) (TL-Comb).
5.1
Experimental Setting
We evaluated our learning algorithms using the video collections officially provided by the TREC video retrieval evaluation(TRECVID) 2002-2005 [Smeaton and Over, 2003].
Video shots are used as the retrieval unit. For each query,
average precision is adopted as a measure of retrieval effectiveness. In more details, let R be the number of true relevant
documents in a set of size S. At any given index j let Rj be
the number of relevant documents in the top j documents. Let
Ij = 1 if the j th document is relevant and 0 otherwise. The
S R
average precision (AP) is then defined as R1 j=1 jj ∗ Ij .
Mean average precision (Mean-AP) is the mean of average
precision for all queries in the collection.
We split the four video collections, i.e., TREC’02-’05, into
a development set to learn model parameters, and a search set
to evaluate retrieval performance. For each search set, NIST
officially provided 25 query topics, including both text description and image/video examples, together with their relevance judgment. On the other hand, the four development
collections are combined into a single training corpus. Several human annotators collaboratively defined 88 query topics
– which are different from the testing queries – and collected
Data Set
Query Num
Doc Num
h=1
In case we want to reduce the number of parameters we can
assume that Ψ is diagonal with isotropic variance, e.g. Ψ =
τ 2 I, and we have τ̂ 2 = Tr(Ψ̂)/F . The EM learning process
is summarized in Algorithm 1.
(k)
update ξi (i = 1, . . . , nk ) based on Eqn(3)
update V(k) and m(k) based on Eqn(4) and Eqn(5)
update φ(k) based on Eqn(6)
continue (a)-(c) until convergence
t02
25
24263
t03
25
75850
t04
24
48818
t05
24
77979
dev
88
124097
Table 1: Labels of the video collections and statistics. t ∗ ∗ indicate
the TRECVID testing sets, where the embedded number is the year,
and dev is the development set.
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Data
t02
t03
t04
t05
Method
STL
TL-SC(H=1)
TL-MC(H=6)
TL-Comb(H=6)
TL-TF(H=6)
STL
TL-SC(H=1)
TL-MC(H=6)*
TL-Comb(H=6)*
TL-TF(H=6)*
STL
TL-SC(H=1)
TL-MC(H=6)
TL-Comb(H=6)
TL-TF(H=6)*
STL
TL-SC(H=1)
TL-MC(H=6)
TL-Comb(H=6)
TL-TF(H=6)
Mean-AP
0.114(+0%)
0.119(+4%)
0.123(+8%)
0.124(+9%)
0.136(+19%)
0.150(+0%)
0.177(+18%)
0.192(+28%)
0.190(+27%)
0.203(+35%)
0.079(+0%)
0.089(+12%)
0.093(+17%)
0.094(+17%)
0.109(+39%)
0.095(+0%)
0.095(+0%)
0.097(+2%)
0.099(+4%)
0.118(+21%)
P30
0.135
0.123
0.132
0.132
0.138
0.212
0.224
0.228
0.227
0.243
0.177
0.186
0.185
0.186
0.190
0.238
0.242
0.240
0.242
0.243
P100
0.081
0.081
0.083
0.084
0.082
0.136
0.134
0.140
0.139
0.136
0.116
0.114
0.110
0.111
0.123
0.205
0.198
0.195
0.194
0.207
Person
0.199
0.290
0.293
0.293
0.387
0.251
0.366
0.428
0.429
0.460
0.144
0.178
0.185
0.186
0.252
0.164
0.159
0.139
0.141
0.180
SObj
0.205
0.183
0.206
0.206
0.208
0.293
0.314
0.350
0.350
0.345
0.063
0.067
0.036
0.037
0.069
0.029
0.021
0.021
0.020
0.047
GObj
0.074
0.062
0.059
0.059
0.049
0.095
0.103
0.081
0.080
0.096
0.034
0.037
0.038
0.037
0.045
0.090
0.091
0.075
0.077
0.072
Sport
0.007
0.017
0.009
0.009
0.006
0.101
0.070
0.102
0.100
0.109
0.108
0.085
0.100
0.099
0.111
0.271
0.200
0.293
0.294
0.329
Other
0.019
0.018
0.020
0.021
0.026
0.012
0.012
0.013
0.013
0.014
0.051
0.061
0.035
0.035
0.047
0.017
0.019
0.016
0.016
0.015
Table 2: Comparison of retrieval performance between STL, TL-SC, TL-MC, TL-Comb and TL-TF on multiple testing sets.
All parameters are learned from the development set with the 88 training queries. * means statistical significance over STL
with p-value < 0.01 (sign tests).
their relevance judgment on the development set. Table 1
lists the labels of video collections and their query/document
statistics.
As building blocks for information retrieval, we generated
a number of ranking features on each video document, including 14 high-level semantic features learned from development
data (face, anchor, commercial, studio, graphics, weather,
sports, outdoor, person, crowd, road, car, building, motion),
and 5 uni-modal retrieval experts (text retrieval, face recognition, image-based retrieval based on color, texture and edge
histograms) [Yan et al., 2004]. For the transfer learning algorithms, the covariance matrix Ψ is initialized to an identity matrix. The parameters of γ h and λh are initialized to
random values uniformly sampled from [0, 1]. The EM algorithm stops when the relative change of the log-likelihood is
less than 10−5 .
We also designed the following 10 binary task features for
the TL-TF model, which indicate if the query topics contain
(1) specific person names; (2) specific object names; (3) more
than two noun phrases; (4) words related to people/crowd; (5)
words related to sports; (6) words related to vehicle; (7) words
related to motion; (8) similar image examples; (9) image examples with faces; (10) if the text retrieval module finds more
than 100 documents. All these task features can be automatically detected from the query description through manually
defined rules plus natural language processing and image processing techniques [Yan et al., 2004].
5.2
Retrieval Results
We present the information retrieval results on all the testing sets using the proposed models and parameters learned
from the development collection. The number of task clusters
can be estimated by optimizing the regularized log-likelihood
with an additional BIC term. Based on development data, we
estimated that the optimal number of task mixtures is 6.
Table 2 provided a detailed comparison between TL-TF
with 6 query clusters (TL-TF, H=6) and several baseline algorithms including single task learning using logistic regression (STL), single-cluster TL (TL-SC, H=1), multi-cluster TL
with 6 clusters(TL-MC, H=6), and TL-Comb with 6 clusters
(TL-Comb, H=6)3 . All the results are reported in terms of the
mean average precisions (Mean-APs) up to 1000 documents,
precision at top 30 and 100 documents. We also grouped the
queries in each collection and reported their Mean-APs in five
different categories, i.e., named person, special object, general object, sports and general queries.
We can observe from the results that TL-MC is usually superior to the STL and TL-SC algorithms, because user queries
are typically organized into a limited number of clusters in the
query feature space. However without task features, TL-MC
needs to assume all new queries share the same parameter
distribution, which limits the flexibility of transfer learning
to produce more accurate results. TL-Comb, which incorporates task features as additional data features, offers slight
gains over TL-MC, but the improvement is limited because it
cannot dynamically change the clustering assignment when
the queries vary. In contrast to TL-MC, TL-TF is able to
leverage more powers from TL by routing new queries to the
correct task clusters. On average, it brings a roughly 4% absolute improvement (or 30% relative improvement) over STL in
terms of mean average precision. As it results, the difference
between TL-TF and STL becomes statistically significant in
two out of four collections. By comparing Mean-APs with
respect to each query type, we find that TL-TF benefits most
from the Person and Special Object type queries, as well as
the Sports type in t05. This is because these query types have
3
All our baseline results are among the top performance in each
year’s TRECVID evaluation
1319
0.12
0.11
0.115
Mean Average Precision
Mean Average Precision
0.115
0.105
0.1
0.095
0.09
0.11
0.105
0.1
0.095
MTL−TF
MTL−MC
0.085
1
2
3
4
5
6
7
8
9
MTL−TF
MTL−MC
0.09
1
10
# of Task Mixtures
2
3
4
5
6
7
8
9
10
# of Task Mixtures
Figure 1: Comparison of TL-TF and TL-MC vs. the number of task clusters on two datasets. Left: t04, Right: t05
their information needs clearly defined and thus they are able
to be improved by making better use of the training data.
To further analyze the performance of the proposed approaches, Figure 1 compares the TL-TF and TL-MC learning
curves on two testing sets with the number of query clusters
growing from 1 to 10. As we can see, TL-TF produces noticeably better results than TL-MC when the task clusters is larger
than 2. The mean average precision of TL-TF increase dramatically using more task clusters especially when the cluster
number is under four. For example, in t05 the mean average
precision is boosted from 9.5% with one cluster to 12% with
four clusters. This clearly shows the benefits of using task
features to model complex task distributions compared with
its non-task-feature counterpart.
6 Conclusion
In this paper, we propose a probabilistic transfer learning
model called TL-TF, of which the basic idea is to use tasklevel features to control the task mixture selection in a hierarchical Bayesian model. In this model, each task predictor is
modeled as a linear combination of a set of basic classifiers,
and the task relatedness is explained by some hidden sources.
We use task features to determine the distribution parameters of these hidden sources via a multi-class logistic regression model. As a result, each task predictor is able to choose
the specific task mixture component more accurately based
on the characteristics described by task features. To estimate
the parameters of TL-TF, we also develop an empirical Bayes
method based on variational approximation techniques. Experimental results on several information retrieval collections
show that the proposed model is much more effective than the
other transfer learning methods that either do not utilize task
features, or simply treat them as data features.
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